Numeric patterns

Memorandum

ACTIVITY 1

Multiples; number patterns; flow diagrams

1. Multiples of 6

• Oral
• Missing multiples of 6

• Oral
• Own answers e.g. they’re all even numbers; they’re all also multiples of 3; some are multiples of 9; some are multiples of 12; they are no prime numbers etc.
• Flow diagram: Output numbers are: 12; 18; 24; 30; 36; 42; 48; 54; 60
• Using the calculator to count in 6’s: press clear; 6 + = = = or 6 + + = = =
• 6; 12; 18; 24; 30; 36; 42; 48; 54; 60; 66; 72; 78; 84; 90; 96; 102
• clear; 102 – 6 = = = or clear; 6 － － 102 = = =

2. Multiples of 7

2.1 Flow diagram – output numbers: 14; 21; 28; 35; 42; 49; 56; 63; 70

• Missing multiples of 7

• Yes
• Own ideas

2.3 105; 98; 91; 84; 77; 70; 63; 56; 49; 42; 35; 28; 21; 14; 7; 0

2.4 Missing multiples of 6 and of 7

2.5 The difference between the multiples of 6 and of 7: 1; 2; 3; …

i.e. 1 x 6 = 6 ; 1 x 7 = 7 the difference between the answers is 1;

2 x 6 = 12 ; 2 x 7 = 14 the difference between the answers is 2;

3 x 6 = 18 ; 3 x 7 = 21 the difference between the answers is 3, etc.

Missing numbers:

1; 5 ; 9

2; 6; 10

3; 7; 11

4; 8; 12

1. Multiples of 8 missing numbers:

32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120

3.2 Flow diagram: missing output numbers: 16; 24; 32; 40; 48; 56; 64; 72; 80

3.3 Missing multiples of 8:

3.4 Oral

3.5 Oral

4. Multiples of 9

4.1 Flow diagram – missing output numbers: 18; 27; 36; 45; 54; 63; 72; 81; 90

• Missing multiples of 9

• Oral

For fun – oral

Test your skills

1. (a) 28, 48, 72, 16

(b) 72, 21, 7, 54

(c) 42, 56, 30, 56

(d) 10, 27, 63, 25

(e) 100, 16, 81, 24

(f) 18, 40, 0, 72

(g) 8, 40, 21, 70

(h) 30, 36, 64, 24

(j) 16, 0, 36, 35

(k) 45, 32, 35, 28

2. Own

ACTIVITY 2

1. Flow diagram – multiples of 8, mixed up

Missing output numbers: 16; 72; 32; 48; 64; 56; 40; 24; 80

2. Own

3. Own

4. Own methods of solving multiplication of single digit x single digit.

Test your skills

1. Flow diagram – missing output numbers: 50; 57; 64; 71; 78; 85

2. Flow diagram – missing output numbers: 6; 7; 8; …;11

– missing output numbers: …; 86; 95

3. Flow diagram – missing output numbers: …; 8

– missing output numbers: 28; 40; 46; …; 58; 76

4. Flow diagram – missing output numbers: …; 6; 7

• missing output numbers: 240; 300; …; 480; 540

5. Flow diagram – missing output numbers: …; 6; 7

missing output numbers: 240; 300; …; 480; 540

6. x 60 ≈ x 6 x 10

7. Missing answers

(a) 120 (b) 490 (c) 150 (d) 630 (e) 240

(f) 800 (g) 3 600 (h) 4 000 (j) 420 (k) 4 500

ACTIVITY 3 – estimations and calculations

1.1 126; 7 x 20 = 140 or 10 x 18 = 180

1.2 144 20 x 6 = 120 or 24 x 10 = 240 or 20 x 10 = 200

1.3 1 944 40 x 50 = 2 000

2. Word sums

2.1 6 Smarties

2.2 7 vehicles

2.3 17 trays and 4 apples left over

3.

3.1 2 000 kg: 2 000 + 500

3.2 20 bags: 25 x 20 = 500

3.3 715 km: rounding off: 60 x 10 = 600 (various methods of checking)

3.4 605 km; rounding off: 60 x 10 = 600

3.5 307 km 899 km + 307 km = 762 km + 444 km

3.6 17 rondavels; 17 x 8 = 80 + 56 = 136

3.7 R39: 39 x 7 = 210 + 63 = 273

3.8 I – I – I – I – I – I : 51 m